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Child fares are mainly available on international flights, not domestic.
Virgin Australia, Jetstar and REX do not offer child discounts. Qantas offers child discounts for the Super Saver fare category and higher. A full paying adult must be travelling with the child for the fare to be valid.
When booking international flights the child fare will be visible by expanding the 'Total Booking Price' at the bottom of the page after you have searched and selected your flights for adult and child passengers.